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Use of internet in teaching of goniometric equations and inequalities
Kepič, Matúš ; Robová, Jarmila (advisor) ; Odvárko, Oldřich (referee)
Title: Use of internet in teaching of goniometric equations and inequalities Author: Matúš Kepič Department: Department of Mathematics Education Supervisor: RNDr. Jarmila Robová, CSc. Supervisor's e-mail address: robova@karlin.mff.cuni.cz Abstract: This work serves as a teaching material for pupils and teachers of secondary school. It deals with subject of goniometrical equations and inequalities. The work contains a theoretical part where is clearly explained the basic theoretical knowledge of the goniometrical equations and inequalities. The emphasis is on practical section that contains the solved examples and the problems for practice which is accompanied by stepping solution. The work has a form of a web application, contains interactive elements (for example. step-by-step solution, multiple choice tests). It is freely accessible on the Internet. The work is accompanied by a CD, where is this thesis in .pdf format. Keywords: trigonometric functions, goniometrical equations, inequalities goniometrical
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Teaching web application for secondary school mathematical logic
Moravec, Luboš ; Odvárko, Oldřich (referee) ; Robová, Jarmila (advisor)
The head part of thís work is a website intended especially for secondary school students which teaches mathematical logic. The website is divided into two parts - a teaching text and tests. The teaching text, which is divided into seven chapters, explains the idea of propositions and their negations, basic logic connectives (conjunction , disjunction, implication, equivalence), a problem of finding truth value of composite propositions and their negations, work with quantifiers, set operations, Venn's diagrams and proof techniques. Except the teaching chapters there are also tests for verifing new knowledge. The questions in tests are randomly selected from a group of similar questions, so a repeated test has new questions. This text contains an user guide, a programmer documentation and a printed version of teaching chapters.
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Problem solving in middle school mathematics
Vrtišková, Zuzana ; Pavlíková, Pavla (referee) ; Odvárko, Oldřich (advisor)
The aim of this degree thesis was creating a collection of solved exercises in Mathematics. This compilation is for pupils because it contains a lot of solved exercises and for primary school teachers as an inspiration for creating their own exercises. Main accent is placed on connecting Mathematics with real life and with other subjects taught at secondary school. The collection contains a number of problems describing situations from our real lives. The typical exercise of such a situation is buying of all kinds of goods, price reductions of goods, paying for goods in instalments and so on. The whole collection is devided into four parts. The first part contains exercises on usage of maps, determination of distance, usage of time tables and work with text. In the second part there are exercises on usage of plan with gauge and calculations of surfaces and volumes of geometrical objects. The third part contains exercises on price reductions of goods and comparison of values according to given criterion. In the last part we can find exercises on calculations of surfaces and volumes of geometrical objects, buying of all kinds of goods and price reductions of those goods.
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Mathematical problems inspired by the nature
Králíková, Jana ; Šarounová, Alena (referee) ; Odvárko, Oldřich (advisor)
The diploma thesis consists of five exercises, which can be used within mathematical education at secondary schools. In these exercises students get involved with mathematical applications in ordinary life, which they can practically experience. A part of each exercise takes place outdoors, outside of the classroom. Objectives of the exercises are to display both mathematical and practical problems of the application. The topics of exercises are Tree height measuring, The measuring of unreachable distances, The altitude profile of a track, Cryptography and The Tower of Hanoi. I tried to make these exercises to solve real practical problems and to use the secondary school mathematics as much as possible at the same time. Students will use their knowledge in plane geometry, goniometry and trigonometry, functions and their graphs, sequences, series and proof by mathematical induction. Purposes of the exercises are to develop mathematical and logical thinking, to teach how to express the real situation in a mathematical way and to recognize mathematics in other fields of human activity.
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Diagrams in the high school mathematics
Vernerová, Ivana ; Voráčková, Petra (referee) ; Odvárko, Oldřich (advisor)
This dissertation handles about an appearance of diagrams in high school mathematics and their use for solving of different problems. It features several kinds of diagrams, their dissimilarities and their ways of use. It also shows how together cohere logic and set theory. The work can help like a basis for mathematics teachers in high schools, in mathematics seminars or in hobby groups for mathematics. Enclosed is also a CD which includes an electronic form of this work.
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Teaching program for bases of mathematical logic
Moravec, Luboš ; Odvárko, Oldřich (referee) ; Robová, Jarmila (advisor)
Nazev prace: Program pro vyuku zakladu matematickeJogiky Autor: Lubos Moravec Katedra: Katedra didaktiky matematiky Vedouci bakalarske prace: RNDr.Jarmila Kobova, CSc. E-mail vedouci: Robova^karlin.mff.cuni.cz Abstrakt: Nejdulezitejsi cast prace je pocitacovy program urceny pfedevsim pro studenty stfednich skol, ktery slouzi k vyuce zakladu matematicke logiky Aplikace je rozdelena na dve casti - vyklad a testy. Vyklad cleneny do tfi kapitol nejdfive vysvetlujc pojcm vyroku a jeho negacc, dale sc zabyva zakladnimi logickymi spojkami (konjunkce, disjunkce, implikace, ekvivalence). Pote nasleduje popis vyhodnocovani pravdivosti a ncgovani slozenych vyroku a na zaver je probrano vyuziti kvantifikatoru. Kazda kapitola je doplnena testem overujicim nabyte znalosti. Otazky v testech jsou nahodnc vybirany z nekolika variant, coz umoznuje testy nckolikrat opakovat s ruznymi otazkanii. Vlastni text prace obsahuje pfedevsim uzivatelskou a programatorskou dokumentaci. Klicova slova; logika, vyrok, logicka spojka, kvantifikator Title: Teaching program for bases of mathematical logic Author: Lubos Moravec Department: Department of Didactics of Mathematics Supervisor: RNDr. Jarmila Robova, CSc. Supervisor's e-mail address: RobovaO^karlin.mff.cuni.cz Abstract: The most important part of this work is a computer application...
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Real Numbers at High Schools
Červenková, Klára ; Slavík, Antonín (referee) ; Odvárko, Oldřich (advisor)
The aim of this diploma dissertation is to create a textbook with commentary for teachers of mathematics at the high schools on the theme "real numbers". Especially, it is concerned about deeper identification with irrational numbers - to understand the difference between rational and irrational numbers. The attention of the thesis focus particularly on proofs of existence of irrational numbers, on their approximation by rational numbers, and also on the characteristics of infinite sets of numbers - the set of real numbers and some of its infinite subsets. Each chapter of this diploma thesis could be also used for practising other issues of mathematics at high schools e. g. application of Pythagorean theorem, simplification of algebraic terms or operation with sequences and series.
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